Which of the following statements are true or false? Give reason in su

Question

Which of the following statements are true or false? Give reason in support of your answer.

a) When two dice are thrown simultaneously then total number of sample points in the
sample space will be 12.
b) Expected value of a continuous random variable X is defined as
$E(x) = \int_{\infty }^{x}xf(x) dx$
.
c) If X and Y are independent random variable then $V(X - Y) = V(X) - V (Y)$ .
d) If $X \sim B(4,3)$ then variance of X is 12.
e) If probability density function of a normally distributed random variable X is
$f(x) = \frac{1}{6\sqrt{2\pi}}e^{\frac{1}{2}\left ( \frac{x-46}{6} \right )^2}$ , $- \infty <x<\infty$
then variance of X is 36.

29 Feb 2024

Answer :

Word Count : 214

a) When two dice are thrown simultaneously, the sample space consists of all possible outcomes. Each die has 6 sides, so the total number of outcomes is $6 \times 6 = 36$, not 12. Therefore, __________ _______ __________ ______ ________ ______ _________ ___.
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